Question 3 (4 marks) Students at the school who are studying mathematics in Years 7 to 10 can receive one of three grades at the end of the year: distinction (D), credit (C) or pass (P). A regular transition matrix T that represents how students' grades change from year to year is given below. Four of the values are listed as j, k, 1 and m. this year D C 0.65 0.29 1 D T= j k 0.38 C next year 0.03 0.09 m P a. Explain the meaning of the value 0.29 in the transition matrix T. 1 mark b. Show that the value of k is 0.62 C. 1 mark Let So be the state matrix that shows the number of students achieving D, C or P in Year 7 General Mathematics at the end of 2017. 80 D S=100 C 50 P All of these students completed Year 8 in 2018, with a total of 82 students receiving a distinction. Using this information, determine the value of 1 in transition matrix T. i. 1 mark ii. Students must achieve a distinction in General Mathematics at the end of Year 10 to qualify for Year 11 Advanced Mathematics. All students who completed Year 7 in 2017 also completed Year 10 in 2020. How many of the Year 7 students from 2017 were predicted to qualify for Year 11 Advanced Mathematics in 2021? Round your answer to the nearest whole number. 1 mark